Everyone's explanations are pretty much spot-on, but I feel like they keep dancing around the issue. Let me spell it out simply...

In general, with very few exceptions: the higher the item level of a piece of gear, the more stats that piece has, and the stronger it is.

Actual level requirements for wearing gear don't really matter when it comes to stats. Just go by item level.

Note: In general, what I stated above is true. But not always. Item level is a value that determines a gear piece's maximum stats, not its base stats. Very few pieces of gear have stats that match its maximum stats. In the case of NQ white gear, for example, they may only be around 80% of the way toward their max stats. So, unless you intend to perfectly meld materia into that white gear, it will never reach the potential stats that its item level implies. Due to this, some green, blue, or purple gear (which have base stats closer to their stat caps than white gear does) can have higher base stats than white gear of a higher item level.

Ultimately, though, you don't need to know all this. As long as you follow common sense - higher attributes (and item level) are better - you'll be set with your gear for all but the hardest of content.